Using Ehrenfest Dynamics to model a particle in a box with moving walls

Omid Hamidi, H. Dehghan

Mohsen Razavy

Vidal Alonso Secades, Salvatore De Vincenzo, L. A. González-Díaz

Daniel S. Rokhsar

Ehrenfest’s theorem states that as a quantum state evolves in time, the rate of change of the expectation value of momentum is equal to the expectation value of the force. In the familiar ‘‘particle-in-a-box,’’ however, the probability of finding the particle at a wall—the only place where forces act—is zero, so at first glance it appears that the expectation value of the force should vanish for any state, which would violate Ehrenfest‘s theorem. This argument is flawed, however, since the forces at the walls of the box are infinite. We consider the box as a limit of a very deep square well and confirm that Ehrenfest’s theorem emerges safe and sound.

Lan Chen, Hongwei Sun, Cheng-Ming LAI

Sara Di Martino, Paolo Facchi A, ANTONINO MESSINA +2 more

We analyze the non-relativistic problem of a quantum particle that bounces back and forth between two moving walls. We recast this problem into the equivalent one of a quantum particle in a fixed box whose dynamics is governed by an appropriate time-dependent Schroedinger operator.